Can You Hear the Shape of a Drum?

If you had perfect pitch and listened to a recording of the sounds a drum made when struck, could you determine the shape of the drum? This question is an example of an inverse problem; inverse problems arise in medical imaging, oil prospecting, spectroscopy, and many other fields. We’ll first discuss the analogous question in the simpler setting of plucking a string. Then we’ll tackle the problem for drums and see that there are some surprises. Finally, I will give a brief indication of how this problem relates to some of my recent research. The emphasis will be on the ideas rather than on the technical details, so there will be pretty pictures instead of equations.

Mapping the Operation of the Miniature Combustion Aerosol Standard (Mini-CAST) Soot Generator

The Jing Ltd. miniature combustion aerosol standard (Mini-CAST) soot generator is a portable, commercially available burner that is widely used for laboratory measurements of soot processes. While many studies have used the Mini-CAST to generate soot with known size, concentration, and organic carbon fraction under a single or few conditions, there has been no systematic study of the burner operation over a wide range of operating conditions. Here, we present a comprehensive characterization of the microphysical, chemical, morphological, and hygroscopic properties of Mini-CAST soot over the full range of oxidation air and mixing N-2 flow rates. Very fuel-rich and fuel-lean flame conditions are found to produce organic-dominated soot with mode diameters of 10-60nm, and the highest particle number concentrations are produced under fuel-rich conditions. The lowest organic fraction and largest diameter soot (70-130nm) occur under slightly fuel-lean conditions. Moving from fuel-rich to fuel-lean conditions also increases the O:C ratio of the soot coatings from similar to 0.05 to similar to 0.25, which causes a small fraction of the particles to act as cloud condensation nuclei near the Kelvin limit (kappa similar to 0-10(-3)). Comparison of these property ranges to those reported in the literature for aircraft and diesel engine soots indicates that the Mini-CAST soot is similar to real-world primary soot particles, which lends itself to a variety of process-based soot studies. The trends in soot properties uncovered here will guide selection of burner operating conditions to achieve optimum soot properties that are most relevant to such studies.

Running in Heels: an Analysis of Advertisements By Female Senate Candidates

Female candidates have become more successful in the political arena, specifically in the United States Senate. Today, females make up twenty percent of the total Senate seats. Despite this increase, females are still underrepresented in Washington. As such, understanding the roadblocks to equality will help us achieve parity. In an attempt to understand various challenges that female senatorial candidates face, this project looks at a specific element of their campaign, TV advertisements. Assessing candidate advertisements will help us understand whether gender affects strategic campaign decisions. Specifically, this project investigates the relationship between candidate gender and casting and setting of TV advertisements. Does gender influence the makeup of political ad spots? In order to understand this relationship more completely, I employ both quantitative data and case study analysis for same-gender and mixed-gender primary and general election contests in 2004 and 2008. Ultimately, candidate gender has little to no effect on casting of senatorial advertisements across both election cycles. Despite this variation in casting, we observe consistent findings across three settings, the political setting, the home setting, and the neighborhood setting. In both 2004 and 2008, female candidates use smaller proportions of ad frames with the political setting in comparison to their male counterparts. Female candidates in both election cycles also employed greater proportions of ad frames with the home and neighborhood setting compared to male candidates. These discrepancies point to a distinction in advertisement strategy depending on gender of the candidate.

The Differential Usage of Services by Impaired Elderly

Why do some clients use institutional services, while other, with comparable impairment, use community based services? To answer this question, a matching procedure paired clients from the two types of service provision. Sixty-six clients, ages 62 and over, were matched for functional ability as rated on a 6-item ADL scale (Katz, et al., 1970). A discriminant function analysis was performed, with the setting of service provision as the criterion variable. The results indicated that the institutional group was more likely than their community counterparts: (a) to have had previous service contact with other service providers; (b) to have less support available within the community setting from family members or friends; (c) to be more impaired in the areas of mental health and social resources.